Must have the same strain of coyotes around here.
I used to hunt them for the fur, so I learned a little bit about them in the process. I used to hear people blame coyotes for losing livestock, but I have never personally seen a coyote (or pack of coyotes) show any interest at all in living livestock. I think people see a coyote munching on a dead cow and assume the coyote killed it. Mice seem to be their main diet around here, with the occasional rabbit thrown in for variety. They like to hunt what's easy to catch, and not likely to kill them in the attempt. They will scavenge, though, so a dead cow is looked upon as the proverbial free lunch.
As for packs, the only time one is likely to see a pack of coyotes around here is during February when they are mating. Otherwise, lone coyotes are the norm.
What I have seen attack livestock is packs of dogs. Myself and a friend used to have quite the reputation as the local 'bounty' hunters and we used to get requests to find out what was killing someone's livestock. In every instance, we found it to be dogs. They don't have to be wild dogs, either--many wore collars to their funerals.
Coyotes will do in pets, however. I think it's a territorial thing.